Nhận thấy:
\(\dfrac{1}{2}=\dfrac{1}{1!+1},\dfrac{1}{3}=\dfrac{1}{2!+1},\dfrac{1}{7}=\dfrac{1}{3!+1},\dfrac{1}{25}=\dfrac{1}{4!+1}\)
\(\Rightarrow\)Số tiếp theo sẽ là \(\dfrac{1}{5!+1}=\dfrac{1}{121}\)
Điền số tiếp theo vào dãy sau:
\(\dfrac{1}{3},\dfrac{1}{7},\dfrac{1}{13},\dfrac{1}{21},\dfrac{1}{31},....\)
Thực hiện các phép tính :
a) \(9,6.2\dfrac{1}{2}-\left(2.125-1\dfrac{5}{12}\right):\dfrac{1}{4}\)
b) \(\dfrac{5}{18}-1,456:\dfrac{7}{25}+4,5.\dfrac{4}{5}\)
c) \(\left(\dfrac{1}{2}+0,8-1\dfrac{1}{3}\right)\left(2,3\right)+4\dfrac{7}{25}-1,28\)
d) \(\left(-5\right).12:\left[\left(-\dfrac{1}{4}\right)+\dfrac{1}{2}:\left(-2\right)\right]+1\dfrac{1}{3}\)
So sánh các phân số sau:
\(\dfrac{2}{3};\dfrac{3}{4};\dfrac{4}{5};\dfrac{5}{6};\dfrac{6}{7};\dfrac{7}{8};\dfrac{8}{9};\dfrac{9}{10}\)
a) Giả sử phân số \(\dfrac{a}{b}\) là 1 phân số trong dãy phân số trên.Tính số tiếp theo
b)
So sánh 2 phân số \(\dfrac{a}{b}\) và \(\dfrac{a+1}{b+1}\)
Tim x, biet:
a.(3-x)+(2x+7)=2x
b. \(\dfrac{x+1}{2}=\dfrac{1}{3}\)
GIUP MK VS
Tính:
a. \(\left(6-\dfrac{2}{3}+\dfrac{1}{2}\right)-\left(5+\dfrac{5}{3}-\dfrac{3}{2}\right)-\left(3-\dfrac{7}{3}+\dfrac{5}{2}\right)\)
b. \(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
c. \(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{25}{12^2.13^2}\)
a) Chứng minh rằng: \(\dfrac{1}{6}< \dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\)
b) Tìm số nguyên a để: \(\dfrac{2a+9}{a+3}+\dfrac{5a+17}{a+3}-\dfrac{3a}{a+3}\) là số nguyên.
10 Thực hiện các phép tính sau:
a) \(\dfrac{-2}{3}+\dfrac{3}{4}-\dfrac{-1}{6}+\dfrac{-2}{5}\) b) \(\dfrac{-2}{3}+\dfrac{-1}{5}+\dfrac{3}{4}-\dfrac{5}{6}-\dfrac{-7}{10}\)
c)\(\dfrac{1}{2}-\dfrac{-2}{5}+\dfrac{1}{3}+\dfrac{5}{7}-\dfrac{-1}{6}+\dfrac{-4}{35}+\dfrac{1}{41}\) ;
d)\(\dfrac{1}{100.99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)
Chứng minh:
a. \(A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
b.\(B=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}< \dfrac{3}{16}\)
c. \(C=\dfrac{1}{41}+\dfrac{1}{42}+\dfrac{1}{43}+...+\dfrac{1}{79}+\dfrac{1}{80}>\dfrac{7}{12}\)
1. Tính :
a, \(A=\dfrac{\dfrac{1}{3}-\dfrac{5}{2}}{\dfrac{3}{4}-\dfrac{1}{2}}.\dfrac{\dfrac{5}{6}+\dfrac{7}{3}}{1-\dfrac{5}{6}}.\dfrac{\dfrac{-2}{5}+1}{\dfrac{2}{5}-1}\).
b, \(B=\dfrac{\dfrac{1}{3}-\dfrac{4}{5}}{\dfrac{1}{3}+\dfrac{4}{5}}.\dfrac{\dfrac{3}{4}-\dfrac{5}{3}}{\dfrac{3}{4}+\dfrac{5}{3}}:\dfrac{\dfrac{4}{5}-1}{1-\dfrac{2}{3}}\).